Internal Page Links

Is it possible to change the #gk-header, #gk-bottom1, etc. to something more descriptive and personalized like for example #contact, #top, or #'whatever-title'?

It depends. #gk-header is an id for header section - if you have GK Portfolio widget inside - it's not possible (it's possible but you should change theme basic structure).

But if you are using some text widget you can add <div id="contact"> your text widget content inside </div> and then you can change your menu item URL to #contact.